Zansei
Here's one from the annals of self-deprecating quasi-pronouns, found in a 1690 letter from Matsuo Bashō to his student/disciple Kameda Shōshun 亀田小春:
何処持参之芳翰落手、御無事之旨珍重ニ存候。類火之難御のがれ候よし、是又御仕合難申盡候。残生いまだ漂泊やまず、湖水のほとりに夏をいとひ候 [...]
I received your letter from Kasho [another disciple] and am delighted to hear that you are well. The news that you escaped harm in the recent fire, too, is a happiness inexpressible in words. As for my aged self, I am taking refuge from the summer on the shores of the lake [...]
Zansei 残生: literally "remaining life," and apparently originally used that way, before its meaning expanded to also include "old person" ("life have-just-a-little-bit-left-of-er"?), which was then available to refer to the self.
(Letter to Shōshun found on pp116-117 of Bashō Zenshū vol. 8 (ed. Hagino Kiyoshi and Kon Eizō, Tokyo: Kadokawa Shoten, 1964)
Avery:
This sounds oddly like a play on 小生, although I'm not even sure if the two words existed in the same era. What did people even normally call themselves in the 1690s?
Right...